Reception and reconstruction of analog signals are performed in a wide variety of applications, including wireless communication systems, spectrum management applications, radar systems, medical imaging systems and many others. In many of these applications, an information-carrying analog signal is sampled, i.e., converted into digital samples. The information is then reconstructed by processing the digital samples.
The minimum sampling rate needed for perfect reconstruction of an arbitrary sampling method was established by Landau in “Necessary Density Conditions for Sampling and Interpolation of Certain Entire Functions,” Acta Mathematica, volume 17, number 1, July, 1967, pages 37-52, which is incorporated herein by reference.
Various methods for signal sampling and reconstruction are known in the art. Some sampling and reconstruction methods refer to bandpass or band-limited signals, and in particular to multi-band signals, i.e., signals that are confined to a finite set of spectral bands. Methods for sampling bandpass signals are described, for example, by Vaughan et al. in “The Theory of Bandpass Sampling,” IEEE Transactions on Signal Processing, volume 39, September, 1991, pages 1973-1984, and by Kohlenberg in “Exact Interpolation of Band-Limited Functions,” Journal of Applied Physics, volume 24, December, 1953, pages 1432-1435, which are incorporated herein by reference.
Lin and Vaidyanathan describe methods for periodic non-uniform sampling of multi-band signals in “Periodically Non-Uniform Sampling of Bandpass Signals,” IEEE Transactions on Circuits and Systems II, volume 45, number 3, March, 1998, pages 340-351, which is incorporated herein by reference. Methods for sampling and reconstruction of multi-band signals are also described by Herley and Wong in “Minimum Rate Sampling and Reconstruction of Signals with Arbitrary Frequency Support,” IEEE Transactions on Information Theory, volume 45, July, 1999, pages 1555-1564, and by Venkataramani and Bresler in “Perfect reconstruction Formulas and Bounds on Aliasing Error in Sub-Nyquist Nonuniform Sampling of Multiband Signals,” IEEE Transactions on Information Theory, volume 46, September, 2000, pages 2173-2183, which are incorporated herein by reference.
Additional methods for sampling and reconstruction of multi-band signals are described by Feng and Bresler in “Spectrum-Blind Minimum-Rate Sampling and Reconstruction of Multiband Signals,” Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ASSP), May 7-10, 1996, Atlanta, Ga., and by Bresler and Feng in “Spectrum-Blind Minimum-Rate Sampling and Reconstruction of 2-D Multiband Signals,” Proceedings of the IEEE International Conference on Image Processing, Lausanne, Switzerland, Sep. 16-19, 1996, which are incorporated herein by reference.